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Zapiski Nauchnykh Seminarov LOMI, 1974, Volume 47, Pages 182–183 (Mi znsl2780)  
Short communications

A note on the D'Alembert functional equation

A. L. Rukhin
Full-text PDF (173 kB)
Abstract: It is shown that the group analogue of D'Alembert (cosine) functional equation has solutions which are central and symmetrical functions only in the case of abelian group. Necessary and sufficient conditions for representability of the solution in the form $\frac12(U(x)+U(x^{-1}))$ with a homomorphism $U$ are given.
Bibliographic databases:
Document Type: Article
UDC: 517.1
Language: Russian
Citation: A. L. Rukhin, “A note on the D'Alembert functional equation”, Investigations on linear operators and function theory. Part V, Zap. Nauchn. Sem. LOMI, 47, "Nauka", Leningrad. Otdel., Leningrad, 1974, 182–183
Citation in format AMSBIB
\Bibitem{Ruk74}
\by A.~L.~Rukhin
\paper A~note on the D'Alembert functional equation
\inbook Investigations on linear operators and function theory. Part~V
\serial Zap. Nauchn. Sem. LOMI
\yr 1974
\vol 47
\pages 182--183
\publ "Nauka", Leningrad. Otdel.
\publaddr Leningrad
\mathnet{http://mi.mathnet.ru/znsl2780}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=387870}
\zmath{https://zbmath.org/?q=an:0449.39007}
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  • https://www.mathnet.ru/eng/znsl/v47/p182
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